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Normal Distribution

In most of the natural-procedures, random alterations adapts to specific probability distribution which is called as normal distribution. Normal distribution is that probability distribution which is observed commonly by everyone. In the year 1700, mathematicians Laplace and de Moivre used normal distribution. Karl Gauss, a German physicist and mathematician used this distribution for analyzing data of astronomy. Thus, for this reason normal distribution was called as Gaussian distribution became more common among many communities of science.

Another definition of normal distribution is that it is a function of statistics which represents random-variable’s distribution in the form of a symmetrical graph having the shape of a bell.

A normal distribution is having a shape similar to the bell, and for this reason it is also sometimes called as bell curve. One e.g. of bell curve is given below:

Normal Distribution

Normal Distribution - Bell Curve

The curve drawn above represent the graph for a given data which is having a mean of “0” (zero). Normal distribution-curve can also be described with the help of following equation of probability density: -

probability density

Characteristics of Bell Curve

Following are the characteristics of bell curve:

  • Symmetric
  • Extends to - / + infinity
  • Unimodal
  • Area which is below the curve is equal to 1.


We can specify Normal distribution by 2 parameters mentioned below:

  • Standard-deviation
  • Mean

In the theory of probability, Gaussian or normal distribution has been defined as common probability-distribution which is used often as 1st approximation for describing

In the statistics, normal distribution has been considered as the most common probability distribution. This is due to many reasons which are mentioned below:

  • 1st, normal distribution are very amenable analytically, i.e., a person can derive large no. of outcomes which involve this normal distribution in an explicit-form.
  • 2nd, normal distribution develops in the form of the central-limit-theorem’s outcome, which defines that in a mild situation, sum of big no. of the random-variables is spread normally in an approximate manner.
  • Finally, normal distribution’s bell-shape makes the distribution convenient option for simulating or modeling random-variable’s huge variety, which is coming across a practice.

Applications of Normal Distribution

There are many applications of normal distribution in various fields of a business enterprise. Some of the examples are mentioned below:

  • It is generally assumed by the theory of modern-portfolio that the diversified portfolio of asset’s returns follows normal distribution.
  • Procedure variations in the operations-management are often normally distributed.
  • In HR management, the performance of an employee is sometimes normally distributed.

Normal distribution is often used for describing random-variables, particularly those which have symmetrical-unimodal-distributions. In most of the cases, normal distribution, however, is just a rough idea of actual-distribution. Normal distribution is practiced in many fields such as statistics, social science & natural-science. is a pioneer in online tutoring and homework help. Our tutors are highly qualified in their subject areas and have been helping students since 2003. For immediate Normal Distribution homework help, use the homework-help form present on this page. You can also get help with your Normal Distribution homework by writing to

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